Properties

Label 35.5.g.a.8.6
Level $35$
Weight $5$
Character 35.8
Analytic conductor $3.618$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 35.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.61794870793\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 8.6
Character \(\chi\) \(=\) 35.8
Dual form 35.5.g.a.22.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0151985 + 0.0151985i) q^{2} +(8.40408 + 8.40408i) q^{3} +15.9995i q^{4} +(-24.2998 - 5.87527i) q^{5} -0.255459 q^{6} +(-13.0958 + 13.0958i) q^{7} +(-0.486345 - 0.486345i) q^{8} +60.2572i q^{9} +O(q^{10})\) \(q+(-0.0151985 + 0.0151985i) q^{2} +(8.40408 + 8.40408i) q^{3} +15.9995i q^{4} +(-24.2998 - 5.87527i) q^{5} -0.255459 q^{6} +(-13.0958 + 13.0958i) q^{7} +(-0.486345 - 0.486345i) q^{8} +60.2572i q^{9} +(0.458616 - 0.280025i) q^{10} +178.541 q^{11} +(-134.461 + 134.461i) q^{12} +(130.151 + 130.151i) q^{13} -0.398073i q^{14} +(-154.841 - 253.594i) q^{15} -255.978 q^{16} +(219.300 - 219.300i) q^{17} +(-0.915819 - 0.915819i) q^{18} -255.173i q^{19} +(94.0016 - 388.786i) q^{20} -220.116 q^{21} +(-2.71356 + 2.71356i) q^{22} +(-54.1585 - 54.1585i) q^{23} -8.17456i q^{24} +(555.962 + 285.536i) q^{25} -3.95620 q^{26} +(174.324 - 174.324i) q^{27} +(-209.527 - 209.527i) q^{28} +438.959i q^{29} +(6.20760 + 1.50089i) q^{30} -1449.39 q^{31} +(11.6720 - 11.6720i) q^{32} +(1500.48 + 1500.48i) q^{33} +6.66605i q^{34} +(395.167 - 241.284i) q^{35} -964.087 q^{36} +(914.326 - 914.326i) q^{37} +(3.87825 + 3.87825i) q^{38} +2187.60i q^{39} +(8.96069 + 14.6755i) q^{40} -1734.82 q^{41} +(3.34544 - 3.34544i) q^{42} +(-103.893 - 103.893i) q^{43} +2856.58i q^{44} +(354.027 - 1464.24i) q^{45} +1.64625 q^{46} +(1422.27 - 1422.27i) q^{47} +(-2151.26 - 2151.26i) q^{48} -343.000i q^{49} +(-12.7895 + 4.11008i) q^{50} +3686.03 q^{51} +(-2082.36 + 2082.36i) q^{52} +(3305.54 + 3305.54i) q^{53} +5.29893i q^{54} +(-4338.52 - 1048.98i) q^{55} +12.7381 q^{56} +(2144.50 - 2144.50i) q^{57} +(-6.67152 - 6.67152i) q^{58} -4661.12i q^{59} +(4057.39 - 2477.39i) q^{60} -3974.31 q^{61} +(22.0285 - 22.0285i) q^{62} +(-789.116 - 789.116i) q^{63} -4095.29i q^{64} +(-2397.97 - 3927.32i) q^{65} -45.6100 q^{66} +(-3729.40 + 3729.40i) q^{67} +(3508.69 + 3508.69i) q^{68} -910.305i q^{69} +(-2.33878 + 9.67310i) q^{70} -1249.55 q^{71} +(29.3058 - 29.3058i) q^{72} +(-3437.16 - 3437.16i) q^{73} +27.7928i q^{74} +(2272.69 + 7072.02i) q^{75} +4082.66 q^{76} +(-2338.14 + 2338.14i) q^{77} +(-33.2482 - 33.2482i) q^{78} +11135.9i q^{79} +(6220.21 + 1503.94i) q^{80} +7810.90 q^{81} +(26.3666 - 26.3666i) q^{82} +(3632.77 + 3632.77i) q^{83} -3521.76i q^{84} +(-6617.39 + 4040.50i) q^{85} +3.15802 q^{86} +(-3689.05 + 3689.05i) q^{87} +(-86.8327 - 86.8327i) q^{88} -8157.71i q^{89} +(16.8736 + 27.6349i) q^{90} -3408.86 q^{91} +(866.511 - 866.511i) q^{92} +(-12180.8 - 12180.8i) q^{93} +43.2326i q^{94} +(-1499.21 + 6200.67i) q^{95} +196.185 q^{96} +(4381.16 - 4381.16i) q^{97} +(5.21308 + 5.21308i) q^{98} +10758.4i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} + O(q^{10}) \) \( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0151985 + 0.0151985i −0.00379962 + 0.00379962i −0.709004 0.705204i \(-0.750855\pi\)
0.705204 + 0.709004i \(0.250855\pi\)
\(3\) 8.40408 + 8.40408i 0.933787 + 0.933787i 0.997940 0.0641531i \(-0.0204346\pi\)
−0.0641531 + 0.997940i \(0.520435\pi\)
\(4\) 15.9995i 0.999971i
\(5\) −24.2998 5.87527i −0.971993 0.235011i
\(6\) −0.255459 −0.00709608
\(7\) −13.0958 + 13.0958i −0.267261 + 0.267261i
\(8\) −0.486345 0.486345i −0.00759914 0.00759914i
\(9\) 60.2572i 0.743916i
\(10\) 0.458616 0.280025i 0.00458616 0.00280025i
\(11\) 178.541 1.47555 0.737774 0.675048i \(-0.235877\pi\)
0.737774 + 0.675048i \(0.235877\pi\)
\(12\) −134.461 + 134.461i −0.933760 + 0.933760i
\(13\) 130.151 + 130.151i 0.770125 + 0.770125i 0.978128 0.208004i \(-0.0666965\pi\)
−0.208004 + 0.978128i \(0.566697\pi\)
\(14\) 0.398073i 0.00203098i
\(15\) −154.841 253.594i −0.688184 1.12708i
\(16\) −255.978 −0.999913
\(17\) 219.300 219.300i 0.758823 0.758823i −0.217285 0.976108i \(-0.569720\pi\)
0.976108 + 0.217285i \(0.0697203\pi\)
\(18\) −0.915819 0.915819i −0.00282660 0.00282660i
\(19\) 255.173i 0.706851i −0.935463 0.353426i \(-0.885017\pi\)
0.935463 0.353426i \(-0.114983\pi\)
\(20\) 94.0016 388.786i 0.235004 0.971965i
\(21\) −220.116 −0.499130
\(22\) −2.71356 + 2.71356i −0.00560653 + 0.00560653i
\(23\) −54.1585 54.1585i −0.102379 0.102379i 0.654062 0.756441i \(-0.273064\pi\)
−0.756441 + 0.654062i \(0.773064\pi\)
\(24\) 8.17456i 0.0141920i
\(25\) 555.962 + 285.536i 0.889540 + 0.456857i
\(26\) −3.95620 −0.00585237
\(27\) 174.324 174.324i 0.239128 0.239128i
\(28\) −209.527 209.527i −0.267254 0.267254i
\(29\) 438.959i 0.521949i 0.965346 + 0.260975i \(0.0840439\pi\)
−0.965346 + 0.260975i \(0.915956\pi\)
\(30\) 6.20760 + 1.50089i 0.00689734 + 0.00166765i
\(31\) −1449.39 −1.50821 −0.754103 0.656757i \(-0.771928\pi\)
−0.754103 + 0.656757i \(0.771928\pi\)
\(32\) 11.6720 11.6720i 0.0113984 0.0113984i
\(33\) 1500.48 + 1500.48i 1.37785 + 1.37785i
\(34\) 6.66605i 0.00576648i
\(35\) 395.167 241.284i 0.322585 0.196967i
\(36\) −964.087 −0.743895
\(37\) 914.326 914.326i 0.667879 0.667879i −0.289346 0.957225i \(-0.593438\pi\)
0.957225 + 0.289346i \(0.0934377\pi\)
\(38\) 3.87825 + 3.87825i 0.00268577 + 0.00268577i
\(39\) 2187.60i 1.43826i
\(40\) 8.96069 + 14.6755i 0.00560043 + 0.00917219i
\(41\) −1734.82 −1.03202 −0.516008 0.856584i \(-0.672582\pi\)
−0.516008 + 0.856584i \(0.672582\pi\)
\(42\) 3.34544 3.34544i 0.00189651 0.00189651i
\(43\) −103.893 103.893i −0.0561885 0.0561885i 0.678454 0.734643i \(-0.262650\pi\)
−0.734643 + 0.678454i \(0.762650\pi\)
\(44\) 2856.58i 1.47551i
\(45\) 354.027 1464.24i 0.174828 0.723081i
\(46\) 1.64625 0.000778003
\(47\) 1422.27 1422.27i 0.643851 0.643851i −0.307649 0.951500i \(-0.599542\pi\)
0.951500 + 0.307649i \(0.0995423\pi\)
\(48\) −2151.26 2151.26i −0.933706 0.933706i
\(49\) 343.000i 0.142857i
\(50\) −12.7895 + 4.11008i −0.00511580 + 0.00164403i
\(51\) 3686.03 1.41716
\(52\) −2082.36 + 2082.36i −0.770102 + 0.770102i
\(53\) 3305.54 + 3305.54i 1.17677 + 1.17677i 0.980563 + 0.196204i \(0.0628614\pi\)
0.196204 + 0.980563i \(0.437139\pi\)
\(54\) 5.29893i 0.00181719i
\(55\) −4338.52 1048.98i −1.43422 0.346770i
\(56\) 12.7381 0.00406191
\(57\) 2144.50 2144.50i 0.660049 0.660049i
\(58\) −6.67152 6.67152i −0.00198321 0.00198321i
\(59\) 4661.12i 1.33902i −0.742804 0.669509i \(-0.766505\pi\)
0.742804 0.669509i \(-0.233495\pi\)
\(60\) 4057.39 2477.39i 1.12705 0.688164i
\(61\) −3974.31 −1.06808 −0.534038 0.845460i \(-0.679326\pi\)
−0.534038 + 0.845460i \(0.679326\pi\)
\(62\) 22.0285 22.0285i 0.00573061 0.00573061i
\(63\) −789.116 789.116i −0.198820 0.198820i
\(64\) 4095.29i 0.999827i
\(65\) −2397.97 3927.32i −0.567568 0.929543i
\(66\) −45.6100 −0.0104706
\(67\) −3729.40 + 3729.40i −0.830786 + 0.830786i −0.987624 0.156838i \(-0.949870\pi\)
0.156838 + 0.987624i \(0.449870\pi\)
\(68\) 3508.69 + 3508.69i 0.758801 + 0.758801i
\(69\) 910.305i 0.191200i
\(70\) −2.33878 + 9.67310i −0.000477303 + 0.00197410i
\(71\) −1249.55 −0.247877 −0.123938 0.992290i \(-0.539553\pi\)
−0.123938 + 0.992290i \(0.539553\pi\)
\(72\) 29.3058 29.3058i 0.00565312 0.00565312i
\(73\) −3437.16 3437.16i −0.644992 0.644992i 0.306786 0.951779i \(-0.400746\pi\)
−0.951779 + 0.306786i \(0.900746\pi\)
\(74\) 27.7928i 0.00507538i
\(75\) 2272.69 + 7072.02i 0.404033 + 1.25725i
\(76\) 4082.66 0.706831
\(77\) −2338.14 + 2338.14i −0.394357 + 0.394357i
\(78\) −33.2482 33.2482i −0.00546486 0.00546486i
\(79\) 11135.9i 1.78431i 0.451731 + 0.892154i \(0.350807\pi\)
−0.451731 + 0.892154i \(0.649193\pi\)
\(80\) 6220.21 + 1503.94i 0.971909 + 0.234990i
\(81\) 7810.90 1.19050
\(82\) 26.3666 26.3666i 0.00392127 0.00392127i
\(83\) 3632.77 + 3632.77i 0.527329 + 0.527329i 0.919775 0.392446i \(-0.128371\pi\)
−0.392446 + 0.919775i \(0.628371\pi\)
\(84\) 3521.76i 0.499116i
\(85\) −6617.39 + 4040.50i −0.915902 + 0.559239i
\(86\) 3.15802 0.000426990
\(87\) −3689.05 + 3689.05i −0.487389 + 0.487389i
\(88\) −86.8327 86.8327i −0.0112129 0.0112129i
\(89\) 8157.71i 1.02988i −0.857225 0.514942i \(-0.827814\pi\)
0.857225 0.514942i \(-0.172186\pi\)
\(90\) 16.8736 + 27.6349i 0.00208315 + 0.00341172i
\(91\) −3408.86 −0.411649
\(92\) 866.511 866.511i 0.102376 0.102376i
\(93\) −12180.8 12180.8i −1.40834 1.40834i
\(94\) 43.2326i 0.00489278i
\(95\) −1499.21 + 6200.67i −0.166118 + 0.687054i
\(96\) 196.185 0.0212874
\(97\) 4381.16 4381.16i 0.465635 0.465635i −0.434862 0.900497i \(-0.643203\pi\)
0.900497 + 0.434862i \(0.143203\pi\)
\(98\) 5.21308 + 5.21308i 0.000542803 + 0.000542803i
\(99\) 10758.4i 1.09768i
\(100\) −4568.44 + 8895.14i −0.456844 + 0.889514i
\(101\) 410.097 0.0402016 0.0201008 0.999798i \(-0.493601\pi\)
0.0201008 + 0.999798i \(0.493601\pi\)
\(102\) −56.0221 + 56.0221i −0.00538466 + 0.00538466i
\(103\) −3073.57 3073.57i −0.289713 0.289713i 0.547254 0.836967i \(-0.315673\pi\)
−0.836967 + 0.547254i \(0.815673\pi\)
\(104\) 126.597i 0.0117046i
\(105\) 5348.79 + 1293.24i 0.485151 + 0.117301i
\(106\) −100.478 −0.00894254
\(107\) 11506.0 11506.0i 1.00498 1.00498i 0.00499151 0.999988i \(-0.498411\pi\)
0.999988 0.00499151i \(-0.00158885\pi\)
\(108\) 2789.11 + 2789.11i 0.239121 + 0.239121i
\(109\) 13007.3i 1.09480i −0.836871 0.547400i \(-0.815618\pi\)
0.836871 0.547400i \(-0.184382\pi\)
\(110\) 81.8819 49.9961i 0.00676710 0.00413191i
\(111\) 15368.1 1.24731
\(112\) 3352.23 3352.23i 0.267238 0.267238i
\(113\) −6514.25 6514.25i −0.510162 0.510162i 0.404414 0.914576i \(-0.367475\pi\)
−0.914576 + 0.404414i \(0.867475\pi\)
\(114\) 65.1863i 0.00501587i
\(115\) 997.846 + 1634.24i 0.0754515 + 0.123572i
\(116\) −7023.15 −0.521934
\(117\) −7842.54 + 7842.54i −0.572908 + 0.572908i
\(118\) 70.8420 + 70.8420i 0.00508777 + 0.00508777i
\(119\) 5743.81i 0.405608i
\(120\) −48.0277 + 198.640i −0.00333526 + 0.0137945i
\(121\) 17236.0 1.17724
\(122\) 60.4036 60.4036i 0.00405829 0.00405829i
\(123\) −14579.6 14579.6i −0.963683 0.963683i
\(124\) 23189.5i 1.50816i
\(125\) −11832.2 10204.9i −0.757260 0.653113i
\(126\) 23.9868 0.00151088
\(127\) 5300.60 5300.60i 0.328638 0.328638i −0.523430 0.852068i \(-0.675348\pi\)
0.852068 + 0.523430i \(0.175348\pi\)
\(128\) 248.994 + 248.994i 0.0151974 + 0.0151974i
\(129\) 1746.24i 0.104936i
\(130\) 96.1350 + 23.2437i 0.00568846 + 0.00137537i
\(131\) −3216.78 −0.187447 −0.0937234 0.995598i \(-0.529877\pi\)
−0.0937234 + 0.995598i \(0.529877\pi\)
\(132\) −24006.9 + 24006.9i −1.37781 + 1.37781i
\(133\) 3341.70 + 3341.70i 0.188914 + 0.188914i
\(134\) 113.362i 0.00631335i
\(135\) −5260.25 + 3211.84i −0.288628 + 0.176233i
\(136\) −213.311 −0.0115328
\(137\) −9320.99 + 9320.99i −0.496616 + 0.496616i −0.910383 0.413767i \(-0.864213\pi\)
0.413767 + 0.910383i \(0.364213\pi\)
\(138\) 13.8353 + 13.8353i 0.000726489 + 0.000726489i
\(139\) 10358.2i 0.536111i 0.963404 + 0.268055i \(0.0863810\pi\)
−0.963404 + 0.268055i \(0.913619\pi\)
\(140\) 3860.44 + 6322.49i 0.196961 + 0.322576i
\(141\) 23905.7 1.20244
\(142\) 18.9912 18.9912i 0.000941838 0.000941838i
\(143\) 23237.3 + 23237.3i 1.13636 + 1.13636i
\(144\) 15424.5i 0.743852i
\(145\) 2579.00 10666.6i 0.122664 0.507331i
\(146\) 104.479 0.00490146
\(147\) 2882.60 2882.60i 0.133398 0.133398i
\(148\) 14628.8 + 14628.8i 0.667860 + 0.667860i
\(149\) 3719.04i 0.167517i 0.996486 + 0.0837584i \(0.0266924\pi\)
−0.996486 + 0.0837584i \(0.973308\pi\)
\(150\) −142.026 72.9427i −0.00631225 0.00324190i
\(151\) −22024.4 −0.965940 −0.482970 0.875637i \(-0.660442\pi\)
−0.482970 + 0.875637i \(0.660442\pi\)
\(152\) −124.102 + 124.102i −0.00537146 + 0.00537146i
\(153\) 13214.4 + 13214.4i 0.564500 + 0.564500i
\(154\) 71.0725i 0.00299682i
\(155\) 35219.8 + 8515.53i 1.46596 + 0.354444i
\(156\) −35000.6 −1.43822
\(157\) −11748.5 + 11748.5i −0.476634 + 0.476634i −0.904053 0.427420i \(-0.859423\pi\)
0.427420 + 0.904053i \(0.359423\pi\)
\(158\) −169.248 169.248i −0.00677970 0.00677970i
\(159\) 55560.0i 2.19770i
\(160\) −352.203 + 215.051i −0.0137579 + 0.00840044i
\(161\) 1418.50 0.0547239
\(162\) −118.714 + 118.714i −0.00452347 + 0.00452347i
\(163\) 5346.78 + 5346.78i 0.201241 + 0.201241i 0.800532 0.599290i \(-0.204550\pi\)
−0.599290 + 0.800532i \(0.704550\pi\)
\(164\) 27756.3i 1.03199i
\(165\) −27645.6 45277.0i −1.01545 1.66307i
\(166\) −110.425 −0.00400731
\(167\) −6998.41 + 6998.41i −0.250938 + 0.250938i −0.821355 0.570417i \(-0.806782\pi\)
0.570417 + 0.821355i \(0.306782\pi\)
\(168\) 107.052 + 107.052i 0.00379296 + 0.00379296i
\(169\) 5317.59i 0.186184i
\(170\) 39.1648 161.984i 0.00135518 0.00560498i
\(171\) 15376.0 0.525838
\(172\) 1662.23 1662.23i 0.0561869 0.0561869i
\(173\) −32836.2 32836.2i −1.09714 1.09714i −0.994744 0.102392i \(-0.967350\pi\)
−0.102392 0.994744i \(-0.532650\pi\)
\(174\) 112.136i 0.00370379i
\(175\) −11020.1 + 3541.45i −0.359840 + 0.115639i
\(176\) −45702.6 −1.47542
\(177\) 39172.5 39172.5i 1.25036 1.25036i
\(178\) 123.985 + 123.985i 0.00391317 + 0.00391317i
\(179\) 4157.69i 0.129761i −0.997893 0.0648807i \(-0.979333\pi\)
0.997893 0.0648807i \(-0.0206667\pi\)
\(180\) 23427.2 + 5664.27i 0.723060 + 0.174823i
\(181\) 48603.7 1.48359 0.741793 0.670629i \(-0.233976\pi\)
0.741793 + 0.670629i \(0.233976\pi\)
\(182\) 51.8096 51.8096i 0.00156411 0.00156411i
\(183\) −33400.5 33400.5i −0.997356 0.997356i
\(184\) 52.6794i 0.00155598i
\(185\) −27589.9 + 16846.1i −0.806132 + 0.492215i
\(186\) 370.258 0.0107023
\(187\) 39154.1 39154.1i 1.11968 1.11968i
\(188\) 22755.6 + 22755.6i 0.643832 + 0.643832i
\(189\) 4565.83i 0.127819i
\(190\) −71.4550 117.027i −0.00197936 0.00324173i
\(191\) −59079.1 −1.61945 −0.809724 0.586811i \(-0.800383\pi\)
−0.809724 + 0.586811i \(0.800383\pi\)
\(192\) 34417.2 34417.2i 0.933625 0.933625i
\(193\) 41523.8 + 41523.8i 1.11476 + 1.11476i 0.992498 + 0.122264i \(0.0390156\pi\)
0.122264 + 0.992498i \(0.460984\pi\)
\(194\) 133.174i 0.00353848i
\(195\) 12852.7 53158.3i 0.338008 1.39798i
\(196\) 5487.84 0.142853
\(197\) 14556.7 14556.7i 0.375085 0.375085i −0.494240 0.869325i \(-0.664554\pi\)
0.869325 + 0.494240i \(0.164554\pi\)
\(198\) −163.512 163.512i −0.00417079 0.00417079i
\(199\) 68770.5i 1.73658i 0.496053 + 0.868292i \(0.334782\pi\)
−0.496053 + 0.868292i \(0.665218\pi\)
\(200\) −131.521 409.258i −0.00328801 0.0102315i
\(201\) −62684.3 −1.55155
\(202\) −6.23286 + 6.23286i −0.000152751 + 0.000152751i
\(203\) −5748.52 5748.52i −0.139497 0.139497i
\(204\) 58974.7i 1.41712i
\(205\) 42155.8 + 10192.5i 1.00311 + 0.242535i
\(206\) 93.4271 0.00220160
\(207\) 3263.44 3263.44i 0.0761614 0.0761614i
\(208\) −33315.8 33315.8i −0.770058 0.770058i
\(209\) 45559.0i 1.04299i
\(210\) −100.949 + 61.6382i −0.00228909 + 0.00139769i
\(211\) −40600.3 −0.911935 −0.455968 0.889996i \(-0.650707\pi\)
−0.455968 + 0.889996i \(0.650707\pi\)
\(212\) −52887.1 + 52887.1i −1.17673 + 1.17673i
\(213\) −10501.3 10501.3i −0.231464 0.231464i
\(214\) 349.748i 0.00763708i
\(215\) 1914.17 + 3134.97i 0.0414099 + 0.0678197i
\(216\) −169.563 −0.00363433
\(217\) 18980.9 18980.9i 0.403085 0.403085i
\(218\) 197.692 + 197.692i 0.00415983 + 0.00415983i
\(219\) 57772.4i 1.20457i
\(220\) 16783.2 69414.4i 0.346760 1.43418i
\(221\) 57084.2 1.16878
\(222\) −233.573 + 233.573i −0.00473932 + 0.00473932i
\(223\) 21915.3 + 21915.3i 0.440695 + 0.440695i 0.892246 0.451550i \(-0.149129\pi\)
−0.451550 + 0.892246i \(0.649129\pi\)
\(224\) 305.708i 0.00609272i
\(225\) −17205.6 + 33500.7i −0.339864 + 0.661743i
\(226\) 198.014 0.00387685
\(227\) −30850.1 + 30850.1i −0.598694 + 0.598694i −0.939965 0.341271i \(-0.889143\pi\)
0.341271 + 0.939965i \(0.389143\pi\)
\(228\) 34311.0 + 34311.0i 0.660029 + 0.660029i
\(229\) 63623.5i 1.21324i 0.794992 + 0.606620i \(0.207475\pi\)
−0.794992 + 0.606620i \(0.792525\pi\)
\(230\) −40.0037 9.67219i −0.000756214 0.000182839i
\(231\) −39299.9 −0.736491
\(232\) 213.486 213.486i 0.00396636 0.00396636i
\(233\) 29781.5 + 29781.5i 0.548574 + 0.548574i 0.926028 0.377454i \(-0.123200\pi\)
−0.377454 + 0.926028i \(0.623200\pi\)
\(234\) 238.390i 0.00435367i
\(235\) −42917.0 + 26204.6i −0.777130 + 0.474506i
\(236\) 74575.8 1.33898
\(237\) −93586.8 + 93586.8i −1.66616 + 1.66616i
\(238\) −87.2973 87.2973i −0.00154116 0.00154116i
\(239\) 70756.8i 1.23872i −0.785108 0.619359i \(-0.787392\pi\)
0.785108 0.619359i \(-0.212608\pi\)
\(240\) 39636.0 + 64914.4i 0.688125 + 1.12699i
\(241\) 12911.9 0.222308 0.111154 0.993803i \(-0.464545\pi\)
0.111154 + 0.993803i \(0.464545\pi\)
\(242\) −261.962 + 261.962i −0.00447308 + 0.00447308i
\(243\) 51523.2 + 51523.2i 0.872550 + 0.872550i
\(244\) 63587.2i 1.06805i
\(245\) −2015.22 + 8334.84i −0.0335730 + 0.138856i
\(246\) 443.175 0.00732326
\(247\) 33211.1 33211.1i 0.544364 0.544364i
\(248\) 704.901 + 704.901i 0.0114611 + 0.0114611i
\(249\) 61060.2i 0.984826i
\(250\) 334.931 24.7324i 0.00535889 0.000395718i
\(251\) −45510.3 −0.722374 −0.361187 0.932494i \(-0.617628\pi\)
−0.361187 + 0.932494i \(0.617628\pi\)
\(252\) 12625.5 12625.5i 0.198814 0.198814i
\(253\) −9669.53 9669.53i −0.151065 0.151065i
\(254\) 161.122i 0.00249740i
\(255\) −89569.8 21656.4i −1.37747 0.333047i
\(256\) 65517.1 0.999711
\(257\) −28510.9 + 28510.9i −0.431663 + 0.431663i −0.889194 0.457530i \(-0.848734\pi\)
0.457530 + 0.889194i \(0.348734\pi\)
\(258\) 26.5403 + 26.5403i 0.000398718 + 0.000398718i
\(259\) 23947.7i 0.356996i
\(260\) 62835.3 38366.5i 0.929516 0.567552i
\(261\) −26450.5 −0.388287
\(262\) 48.8902 48.8902i 0.000712228 0.000712228i
\(263\) −28724.4 28724.4i −0.415279 0.415279i 0.468294 0.883573i \(-0.344869\pi\)
−0.883573 + 0.468294i \(0.844869\pi\)
\(264\) 1459.50i 0.0209409i
\(265\) −60903.1 99744.9i −0.867256 1.42036i
\(266\) −101.578 −0.00143560
\(267\) 68558.1 68558.1i 0.961692 0.961692i
\(268\) −59668.6 59668.6i −0.830762 0.830762i
\(269\) 56575.8i 0.781855i −0.920422 0.390927i \(-0.872154\pi\)
0.920422 0.390927i \(-0.127846\pi\)
\(270\) 31.1326 128.763i 0.000427059 0.00176630i
\(271\) 85972.1 1.17063 0.585314 0.810807i \(-0.300971\pi\)
0.585314 + 0.810807i \(0.300971\pi\)
\(272\) −56135.9 + 56135.9i −0.758757 + 0.758757i
\(273\) −28648.4 28648.4i −0.384392 0.384392i
\(274\) 283.330i 0.00377391i
\(275\) 99262.3 + 50980.0i 1.31256 + 0.674115i
\(276\) 14564.5 0.191195
\(277\) −52002.6 + 52002.6i −0.677743 + 0.677743i −0.959489 0.281746i \(-0.909087\pi\)
0.281746 + 0.959489i \(0.409087\pi\)
\(278\) −157.429 157.429i −0.00203702 0.00203702i
\(279\) 87335.9i 1.12198i
\(280\) −309.535 74.8400i −0.00394815 0.000954592i
\(281\) 48758.7 0.617503 0.308752 0.951143i \(-0.400089\pi\)
0.308752 + 0.951143i \(0.400089\pi\)
\(282\) −363.330 + 363.330i −0.00456881 + 0.00456881i
\(283\) −80206.3 80206.3i −1.00146 1.00146i −0.999999 0.00146510i \(-0.999534\pi\)
−0.00146510 0.999999i \(-0.500466\pi\)
\(284\) 19992.2i 0.247870i
\(285\) −64710.4 + 39511.4i −0.796681 + 0.486444i
\(286\) −706.345 −0.00863545
\(287\) 22718.8 22718.8i 0.275818 0.275818i
\(288\) 703.322 + 703.322i 0.00847948 + 0.00847948i
\(289\) 12663.7i 0.151623i
\(290\) 122.920 + 201.314i 0.00146159 + 0.00239374i
\(291\) 73639.3 0.869608
\(292\) 54993.1 54993.1i 0.644974 0.644974i
\(293\) −4087.77 4087.77i −0.0476159 0.0476159i 0.682898 0.730514i \(-0.260719\pi\)
−0.730514 + 0.682898i \(0.760719\pi\)
\(294\) 87.6224i 0.00101373i
\(295\) −27385.3 + 113264.i −0.314684 + 1.30152i
\(296\) −889.356 −0.0101506
\(297\) 31124.1 31124.1i 0.352845 0.352845i
\(298\) −56.5238 56.5238i −0.000636501 0.000636501i
\(299\) 14097.6i 0.157689i
\(300\) −113149. + 36361.9i −1.25721 + 0.404022i
\(301\) 2721.11 0.0300340
\(302\) 334.738 334.738i 0.00367021 0.00367021i
\(303\) 3446.49 + 3446.49i 0.0375398 + 0.0375398i
\(304\) 65318.7i 0.706790i
\(305\) 96575.1 + 23350.2i 1.03816 + 0.251009i
\(306\) −401.678 −0.00428978
\(307\) −23151.2 + 23151.2i −0.245639 + 0.245639i −0.819178 0.573539i \(-0.805570\pi\)
0.573539 + 0.819178i \(0.305570\pi\)
\(308\) −37409.2 37409.2i −0.394346 0.394346i
\(309\) 51661.0i 0.541060i
\(310\) −664.711 + 405.865i −0.00691687 + 0.00422336i
\(311\) 30470.3 0.315033 0.157517 0.987516i \(-0.449651\pi\)
0.157517 + 0.987516i \(0.449651\pi\)
\(312\) 1063.93 1063.93i 0.0109296 0.0109296i
\(313\) 12110.0 + 12110.0i 0.123610 + 0.123610i 0.766206 0.642595i \(-0.222142\pi\)
−0.642595 + 0.766206i \(0.722142\pi\)
\(314\) 357.120i 0.00362206i
\(315\) 14539.1 + 23811.7i 0.146527 + 0.239976i
\(316\) −178169. −1.78426
\(317\) 52830.9 52830.9i 0.525738 0.525738i −0.393561 0.919299i \(-0.628757\pi\)
0.919299 + 0.393561i \(0.128757\pi\)
\(318\) −844.429 844.429i −0.00835043 0.00835043i
\(319\) 78372.4i 0.770161i
\(320\) −24060.9 + 99514.8i −0.234970 + 0.971824i
\(321\) 193395. 1.87687
\(322\) −21.5590 + 21.5590i −0.000207930 + 0.000207930i
\(323\) −55959.4 55959.4i −0.536375 0.536375i
\(324\) 124971.i 1.19047i
\(325\) 35196.3 + 109522.i 0.333219 + 1.03689i
\(326\) −162.526 −0.00152928
\(327\) 109315. 109315.i 1.02231 1.02231i
\(328\) 843.720 + 843.720i 0.00784243 + 0.00784243i
\(329\) 37251.4i 0.344153i
\(330\) 1108.31 + 267.971i 0.0101774 + 0.00246070i
\(331\) −67516.0 −0.616241 −0.308121 0.951347i \(-0.599700\pi\)
−0.308121 + 0.951347i \(0.599700\pi\)
\(332\) −58122.7 + 58122.7i −0.527314 + 0.527314i
\(333\) 55094.8 + 55094.8i 0.496846 + 0.496846i
\(334\) 212.730i 0.00190694i
\(335\) 112535. 68712.5i 1.00276 0.612274i
\(336\) 56344.9 0.499087
\(337\) −135510. + 135510.i −1.19320 + 1.19320i −0.217033 + 0.976164i \(0.569638\pi\)
−0.976164 + 0.217033i \(0.930362\pi\)
\(338\) −80.8194 80.8194i −0.000707428 0.000707428i
\(339\) 109493.i 0.952765i
\(340\) −64646.1 105875.i −0.559223 0.915875i
\(341\) −258775. −2.22543
\(342\) −233.693 + 233.693i −0.00199799 + 0.00199799i
\(343\) 4491.86 + 4491.86i 0.0381802 + 0.0381802i
\(344\) 101.055i 0.000853968i
\(345\) −5348.28 + 22120.2i −0.0449341 + 0.185845i
\(346\) 998.121 0.00833741
\(347\) −82622.8 + 82622.8i −0.686185 + 0.686185i −0.961387 0.275202i \(-0.911255\pi\)
0.275202 + 0.961387i \(0.411255\pi\)
\(348\) −59023.1 59023.1i −0.487375 0.487375i
\(349\) 41675.4i 0.342160i −0.985257 0.171080i \(-0.945274\pi\)
0.985257 0.171080i \(-0.0547256\pi\)
\(350\) 113.664 221.314i 0.000927870 0.00180664i
\(351\) 45376.9 0.368316
\(352\) 2083.93 2083.93i 0.0168189 0.0168189i
\(353\) 76506.9 + 76506.9i 0.613976 + 0.613976i 0.943980 0.330004i \(-0.107050\pi\)
−0.330004 + 0.943980i \(0.607050\pi\)
\(354\) 1190.72i 0.00950178i
\(355\) 30363.8 + 7341.42i 0.240934 + 0.0582537i
\(356\) 130520. 1.02985
\(357\) −48271.5 + 48271.5i −0.378751 + 0.378751i
\(358\) 63.1906 + 63.1906i 0.000493045 + 0.000493045i
\(359\) 39385.8i 0.305598i −0.988257 0.152799i \(-0.951171\pi\)
0.988257 0.152799i \(-0.0488287\pi\)
\(360\) −884.304 + 539.946i −0.00682334 + 0.00416625i
\(361\) 65207.6 0.500361
\(362\) −738.704 + 738.704i −0.00563707 + 0.00563707i
\(363\) 144853. + 144853.i 1.09929 + 1.09929i
\(364\) 54540.3i 0.411637i
\(365\) 63328.2 + 103717.i 0.475348 + 0.778508i
\(366\) 1015.27 0.00757916
\(367\) −59666.2 + 59666.2i −0.442992 + 0.442992i −0.893016 0.450024i \(-0.851415\pi\)
0.450024 + 0.893016i \(0.351415\pi\)
\(368\) 13863.4 + 13863.4i 0.102370 + 0.102370i
\(369\) 104535.i 0.767733i
\(370\) 163.290 675.359i 0.00119277 0.00493323i
\(371\) −86577.3 −0.629008
\(372\) 194886. 194886.i 1.40830 1.40830i
\(373\) −151950. 151950.i −1.09215 1.09215i −0.995299 0.0968525i \(-0.969122\pi\)
−0.0968525 0.995299i \(-0.530878\pi\)
\(374\) 1190.17i 0.00850872i
\(375\) −13675.9 185201.i −0.0972507 1.31699i
\(376\) −1383.42 −0.00978542
\(377\) −57131.0 + 57131.0i −0.401966 + 0.401966i
\(378\) −69.3937 69.3937i −0.000485665 0.000485665i
\(379\) 200208.i 1.39381i 0.717165 + 0.696904i \(0.245439\pi\)
−0.717165 + 0.696904i \(0.754561\pi\)
\(380\) −99207.8 23986.7i −0.687035 0.166113i
\(381\) 89093.4 0.613756
\(382\) 897.913 897.913i 0.00615330 0.00615330i
\(383\) 108161. + 108161.i 0.737351 + 0.737351i 0.972065 0.234714i \(-0.0754153\pi\)
−0.234714 + 0.972065i \(0.575415\pi\)
\(384\) 4185.14i 0.0283823i
\(385\) 70553.6 43079.2i 0.475990 0.290634i
\(386\) −1262.20 −0.00847135
\(387\) 6260.27 6260.27i 0.0417995 0.0417995i
\(388\) 70096.6 + 70096.6i 0.465622 + 0.465622i
\(389\) 287702.i 1.90127i −0.310317 0.950633i \(-0.600435\pi\)
0.310317 0.950633i \(-0.399565\pi\)
\(390\) 612.584 + 1003.27i 0.00402751 + 0.00659611i
\(391\) −23753.9 −0.155375
\(392\) −166.816 + 166.816i −0.00108559 + 0.00108559i
\(393\) −27034.0 27034.0i −0.175035 0.175035i
\(394\) 442.480i 0.00285037i
\(395\) 65426.2 270600.i 0.419332 1.73433i
\(396\) −172129. −1.09765
\(397\) −15821.3 + 15821.3i −0.100383 + 0.100383i −0.755515 0.655132i \(-0.772613\pi\)
0.655132 + 0.755515i \(0.272613\pi\)
\(398\) −1045.21 1045.21i −0.00659837 0.00659837i
\(399\) 56167.8i 0.352811i
\(400\) −142314. 73090.9i −0.889463 0.456818i
\(401\) 37856.9 0.235427 0.117714 0.993048i \(-0.462444\pi\)
0.117714 + 0.993048i \(0.462444\pi\)
\(402\) 952.707 952.707i 0.00589532 0.00589532i
\(403\) −188639. 188639.i −1.16151 1.16151i
\(404\) 6561.36i 0.0402005i
\(405\) −189804. 45891.1i −1.15716 0.279781i
\(406\) 174.738 0.00106007
\(407\) 163245. 163245.i 0.985488 0.985488i
\(408\) −1792.68 1792.68i −0.0107692 0.0107692i
\(409\) 16990.5i 0.101569i 0.998710 + 0.0507844i \(0.0161721\pi\)
−0.998710 + 0.0507844i \(0.983828\pi\)
\(410\) −795.615 + 485.793i −0.00473299 + 0.00288991i
\(411\) −156669. −0.927467
\(412\) 49175.6 49175.6i 0.289705 0.289705i
\(413\) 61041.1 + 61041.1i 0.357868 + 0.357868i
\(414\) 99.1987i 0.000578769i
\(415\) −66932.2 109619.i −0.388632 0.636488i
\(416\) 3038.24 0.0175564
\(417\) −87051.1 + 87051.1i −0.500613 + 0.500613i
\(418\) 692.428 + 692.428i 0.00396298 + 0.00396298i
\(419\) 291749.i 1.66181i 0.556413 + 0.830906i \(0.312177\pi\)
−0.556413 + 0.830906i \(0.687823\pi\)
\(420\) −20691.3 + 85578.1i −0.117298 + 0.485137i
\(421\) 105749. 0.596637 0.298319 0.954466i \(-0.403574\pi\)
0.298319 + 0.954466i \(0.403574\pi\)
\(422\) 617.063 617.063i 0.00346501 0.00346501i
\(423\) 85701.8 + 85701.8i 0.478971 + 0.478971i
\(424\) 3215.26i 0.0178848i
\(425\) 184540. 59304.5i 1.02168 0.328329i
\(426\) 319.208 0.00175895
\(427\) 52046.8 52046.8i 0.285456 0.285456i
\(428\) 184091. + 184091.i 1.00495 + 1.00495i
\(429\) 390577.i 2.12223i
\(430\) −76.7393 18.5542i −0.000415031 0.000100347i
\(431\) −193428. −1.04127 −0.520637 0.853778i \(-0.674305\pi\)
−0.520637 + 0.853778i \(0.674305\pi\)
\(432\) −44623.1 + 44623.1i −0.239107 + 0.239107i
\(433\) 123647. + 123647.i 0.659488 + 0.659488i 0.955259 0.295771i \(-0.0955765\pi\)
−0.295771 + 0.955259i \(0.595576\pi\)
\(434\) 576.961i 0.00306314i
\(435\) 111317. 67969.1i 0.588281 0.359197i
\(436\) 208111. 1.09477
\(437\) −13819.8 + 13819.8i −0.0723667 + 0.0723667i
\(438\) 878.054 + 878.054i 0.00457692 + 0.00457692i
\(439\) 120323.i 0.624337i −0.950027 0.312168i \(-0.898945\pi\)
0.950027 0.312168i \(-0.101055\pi\)
\(440\) 1599.85 + 2620.18i 0.00826370 + 0.0135340i
\(441\) 20668.2 0.106274
\(442\) −867.594 + 867.594i −0.00444091 + 0.00444091i
\(443\) 42476.7 + 42476.7i 0.216443 + 0.216443i 0.806998 0.590555i \(-0.201091\pi\)
−0.590555 + 0.806998i \(0.701091\pi\)
\(444\) 245883.i 1.24728i
\(445\) −47928.7 + 198231.i −0.242034 + 1.00104i
\(446\) −666.160 −0.00334895
\(447\) −31255.1 + 31255.1i −0.156425 + 0.156425i
\(448\) 53631.1 + 53631.1i 0.267215 + 0.267215i
\(449\) 58862.3i 0.291974i 0.989286 + 0.145987i \(0.0466358\pi\)
−0.989286 + 0.145987i \(0.953364\pi\)
\(450\) −247.662 770.660i −0.00122302 0.00380573i
\(451\) −309737. −1.52279
\(452\) 104225. 104225.i 0.510147 0.510147i
\(453\) −185095. 185095.i −0.901983 0.901983i
\(454\) 937.751i 0.00454963i
\(455\) 82834.8 + 20028.0i 0.400120 + 0.0967419i
\(456\) −2085.93 −0.0100316
\(457\) 273815. 273815.i 1.31107 1.31107i 0.390438 0.920629i \(-0.372324\pi\)
0.920629 0.390438i \(-0.127676\pi\)
\(458\) −966.981 966.981i −0.00460985 0.00460985i
\(459\) 76458.5i 0.362911i
\(460\) −26147.0 + 15965.1i −0.123568 + 0.0754493i
\(461\) −361733. −1.70210 −0.851052 0.525082i \(-0.824035\pi\)
−0.851052 + 0.525082i \(0.824035\pi\)
\(462\) 597.299 597.299i 0.00279839 0.00279839i
\(463\) −16249.5 16249.5i −0.0758014 0.0758014i 0.668190 0.743991i \(-0.267069\pi\)
−0.743991 + 0.668190i \(0.767069\pi\)
\(464\) 112364.i 0.521904i
\(465\) 224425. + 367555.i 1.03792 + 1.69987i
\(466\) −905.269 −0.00416875
\(467\) −188589. + 188589.i −0.864735 + 0.864735i −0.991884 0.127148i \(-0.959418\pi\)
0.127148 + 0.991884i \(0.459418\pi\)
\(468\) −125477. 125477.i −0.572892 0.572892i
\(469\) 97678.9i 0.444074i
\(470\) 254.003 1050.54i 0.00114986 0.00475575i
\(471\) −197471. −0.890149
\(472\) −2266.91 + 2266.91i −0.0101754 + 0.0101754i
\(473\) −18549.1 18549.1i −0.0829088 0.0829088i
\(474\) 2844.76i 0.0126616i
\(475\) 72861.1 141867.i 0.322930 0.628772i
\(476\) −91898.3 −0.405596
\(477\) −199183. + 199183.i −0.875416 + 0.875416i
\(478\) 1075.40 + 1075.40i 0.00470666 + 0.00470666i
\(479\) 347260.i 1.51351i −0.653701 0.756753i \(-0.726785\pi\)
0.653701 0.756753i \(-0.273215\pi\)
\(480\) −4767.26 1152.64i −0.0206912 0.00500277i
\(481\) 238001. 1.02870
\(482\) −196.241 + 196.241i −0.000844689 + 0.000844689i
\(483\) 11921.2 + 11921.2i 0.0511004 + 0.0511004i
\(484\) 275768.i 1.17721i
\(485\) −132202. + 80721.0i −0.562023 + 0.343165i
\(486\) −1566.15 −0.00663072
\(487\) 35396.5 35396.5i 0.149246 0.149246i −0.628535 0.777781i \(-0.716345\pi\)
0.777781 + 0.628535i \(0.216345\pi\)
\(488\) 1932.89 + 1932.89i 0.00811646 + 0.00811646i
\(489\) 89869.6i 0.375833i
\(490\) −96.0487 157.305i −0.000400036 0.000655166i
\(491\) −180759. −0.749785 −0.374893 0.927068i \(-0.622320\pi\)
−0.374893 + 0.927068i \(0.622320\pi\)
\(492\) 233266. 233266.i 0.963655 0.963655i
\(493\) 96263.7 + 96263.7i 0.396067 + 0.396067i
\(494\) 1009.52i 0.00413675i
\(495\) 63208.5 261427.i 0.257968 1.06694i
\(496\) 371010. 1.50807
\(497\) 16363.8 16363.8i 0.0662479 0.0662479i
\(498\) −928.023 928.023i −0.00374197 0.00374197i
\(499\) 186215.i 0.747847i 0.927460 + 0.373923i \(0.121988\pi\)
−0.927460 + 0.373923i \(0.878012\pi\)
\(500\) 163274. 189310.i 0.653095 0.757238i
\(501\) −117630. −0.468645
\(502\) 691.687 691.687i 0.00274475 0.00274475i
\(503\) −28470.2 28470.2i −0.112526 0.112526i 0.648602 0.761128i \(-0.275354\pi\)
−0.761128 + 0.648602i \(0.775354\pi\)
\(504\) 767.565i 0.00302172i
\(505\) −9965.28 2409.43i −0.0390757 0.00944782i
\(506\) 293.925 0.00114798
\(507\) −44689.5 + 44689.5i −0.173856 + 0.173856i
\(508\) 84807.2 + 84807.2i 0.328629 + 0.328629i
\(509\) 9013.98i 0.0347921i −0.999849 0.0173961i \(-0.994462\pi\)
0.999849 0.0173961i \(-0.00553762\pi\)
\(510\) 1690.47 1032.18i 0.00649931 0.00396840i
\(511\) 90024.9 0.344763
\(512\) −4979.67 + 4979.67i −0.0189959 + 0.0189959i
\(513\) −44482.9 44482.9i −0.169028 0.169028i
\(514\) 866.647i 0.00328032i
\(515\) 56629.1 + 92745.1i 0.213513 + 0.349685i
\(516\) 27939.1 0.104933
\(517\) 253933. 253933.i 0.950033 0.950033i
\(518\) −363.969 363.969i −0.00135645 0.00135645i
\(519\) 551916.i 2.04898i
\(520\) −743.789 + 3076.27i −0.00275070 + 0.0113768i
\(521\) 123697. 0.455704 0.227852 0.973696i \(-0.426830\pi\)
0.227852 + 0.973696i \(0.426830\pi\)
\(522\) 402.007 402.007i 0.00147534 0.00147534i
\(523\) 82201.1 + 82201.1i 0.300521 + 0.300521i 0.841218 0.540697i \(-0.181839\pi\)
−0.540697 + 0.841218i \(0.681839\pi\)
\(524\) 51466.9i 0.187441i
\(525\) −122376. 62851.1i −0.443996 0.228031i
\(526\) 873.135 0.00315580
\(527\) −317850. + 317850.i −1.14446 + 1.14446i
\(528\) −384089. 384089.i −1.37773 1.37773i
\(529\) 273975.i 0.979037i
\(530\) 2441.61 + 590.338i 0.00869209 + 0.00210159i
\(531\) 280866. 0.996117
\(532\) −53465.6 + 53465.6i −0.188909 + 0.188909i
\(533\) −225788. 225788.i −0.794780 0.794780i
\(534\) 2083.96i 0.00730814i
\(535\) −347195. + 211993.i −1.21301 + 0.740652i
\(536\) 3627.55 0.0126265
\(537\) 34941.5 34941.5i 0.121170 0.121170i
\(538\) 859.867 + 859.867i 0.00297075 + 0.00297075i
\(539\) 61239.7i 0.210793i
\(540\) −51388.0 84161.5i −0.176228 0.288620i
\(541\) 17926.3 0.0612484 0.0306242 0.999531i \(-0.490250\pi\)
0.0306242 + 0.999531i \(0.490250\pi\)
\(542\) −1306.65 + 1306.65i −0.00444795 + 0.00444795i
\(543\) 408470. + 408470.i 1.38535 + 1.38535i
\(544\) 5119.33i 0.0172988i
\(545\) −76421.4 + 316075.i −0.257290 + 1.06414i
\(546\) 870.825 0.00292109
\(547\) −336131. + 336131.i −1.12340 + 1.12340i −0.132173 + 0.991227i \(0.542196\pi\)
−0.991227 + 0.132173i \(0.957804\pi\)
\(548\) −149132. 149132.i −0.496602 0.496602i
\(549\) 239481.i 0.794560i
\(550\) −2283.46 + 733.819i −0.00754862 + 0.00242585i
\(551\) 112011. 0.368941
\(552\) −442.722 + 442.722i −0.00145296 + 0.00145296i
\(553\) −145833. 145833.i −0.476876 0.476876i
\(554\) 1580.72i 0.00515034i
\(555\) −373443. 90292.0i −1.21238 0.293132i
\(556\) −165726. −0.536095
\(557\) 178158. 178158.i 0.574241 0.574241i −0.359070 0.933311i \(-0.616906\pi\)
0.933311 + 0.359070i \(0.116906\pi\)
\(558\) 1327.37 + 1327.37i 0.00426309 + 0.00426309i
\(559\) 27043.4i 0.0865443i
\(560\) −101154. + 61763.4i −0.322557 + 0.196950i
\(561\) 658108. 2.09108
\(562\) −741.058 + 741.058i −0.00234628 + 0.00234628i
\(563\) 289503. + 289503.i 0.913348 + 0.913348i 0.996534 0.0831863i \(-0.0265097\pi\)
−0.0831863 + 0.996534i \(0.526510\pi\)
\(564\) 382480.i 1.20240i
\(565\) 120022. + 196568.i 0.375980 + 0.615767i
\(566\) 2438.03 0.00761037
\(567\) −102290. + 102290.i −0.318176 + 0.318176i
\(568\) 607.711 + 607.711i 0.00188365 + 0.00188365i
\(569\) 448419.i 1.38503i −0.721403 0.692516i \(-0.756502\pi\)
0.721403 0.692516i \(-0.243498\pi\)
\(570\) 382.987 1584.01i 0.00117878 0.00487539i
\(571\) 403775. 1.23842 0.619209 0.785226i \(-0.287453\pi\)
0.619209 + 0.785226i \(0.287453\pi\)
\(572\) −371787. + 371787.i −1.13632 + 1.13632i
\(573\) −496506. 496506.i −1.51222 1.51222i
\(574\) 690.584i 0.00209601i
\(575\) −14645.9 45574.3i −0.0442976 0.137843i
\(576\) 246771. 0.743787
\(577\) 314392. 314392.i 0.944321 0.944321i −0.0542087 0.998530i \(-0.517264\pi\)
0.998530 + 0.0542087i \(0.0172636\pi\)
\(578\) 192.470 + 192.470i 0.000576112 + 0.000576112i
\(579\) 697938.i 2.08190i
\(580\) 170661. + 41262.9i 0.507316 + 0.122660i
\(581\) −95148.1 −0.281869
\(582\) −1119.21 + 1119.21i −0.00330418 + 0.00330418i
\(583\) 590175. + 590175.i 1.73638 + 1.73638i
\(584\) 3343.29i 0.00980277i
\(585\) 236649. 144495.i 0.691502 0.422223i
\(586\) 124.256 0.000361845
\(587\) −56100.9 + 56100.9i −0.162815 + 0.162815i −0.783812 0.620998i \(-0.786728\pi\)
0.620998 + 0.783812i \(0.286728\pi\)
\(588\) 46120.3 + 46120.3i 0.133394 + 0.133394i
\(589\) 369844.i 1.06608i
\(590\) −1305.23 2137.66i −0.00374959 0.00614095i
\(591\) 244671. 0.700500
\(592\) −234047. + 234047.i −0.667821 + 0.667821i
\(593\) −65402.5 65402.5i −0.185988 0.185988i 0.607971 0.793959i \(-0.291984\pi\)
−0.793959 + 0.607971i \(0.791984\pi\)
\(594\) 946.078i 0.00268135i
\(595\) 33746.4 139574.i 0.0953222 0.394248i
\(596\) −59502.9 −0.167512
\(597\) −577953. + 577953.i −1.62160 + 1.62160i
\(598\) 214.262 + 214.262i 0.000599159 + 0.000599159i
\(599\) 519621.i 1.44822i 0.689687 + 0.724108i \(0.257748\pi\)
−0.689687 + 0.724108i \(0.742252\pi\)
\(600\) 2334.13 4544.75i 0.00648370 0.0126243i
\(601\) −433485. −1.20012 −0.600060 0.799955i \(-0.704857\pi\)
−0.600060 + 0.799955i \(0.704857\pi\)
\(602\) −41.3568 + 41.3568i −0.000114118 + 0.000114118i
\(603\) −224723. 224723.i −0.618035 0.618035i
\(604\) 352380.i 0.965913i
\(605\) −418832. 101266.i −1.14427 0.276665i
\(606\) −104.763 −0.000285274
\(607\) 374141. 374141.i 1.01545 1.01545i 0.0155710 0.999879i \(-0.495043\pi\)
0.999879 0.0155710i \(-0.00495661\pi\)
\(608\) −2978.38 2978.38i −0.00805700 0.00805700i
\(609\) 96622.1i 0.260521i
\(610\) −1822.68 + 1112.91i −0.00489837 + 0.00299089i
\(611\) 370219. 0.991690
\(612\) −211424. + 211424.i −0.564484 + 0.564484i
\(613\) −152256. 152256.i −0.405186 0.405186i 0.474870 0.880056i \(-0.342495\pi\)
−0.880056 + 0.474870i \(0.842495\pi\)
\(614\) 703.727i 0.00186667i
\(615\) 268622. + 439939.i 0.710217 + 1.16317i
\(616\) 2274.29 0.00599355
\(617\) 408731. 408731.i 1.07366 1.07366i 0.0766005 0.997062i \(-0.475593\pi\)
0.997062 0.0766005i \(-0.0244066\pi\)
\(618\) 785.169 + 785.169i 0.00205583 + 0.00205583i
\(619\) 72206.4i 0.188449i −0.995551 0.0942247i \(-0.969963\pi\)
0.995551 0.0942247i \(-0.0300372\pi\)
\(620\) −136244. + 563500.i −0.354434 + 1.46592i
\(621\) −18882.3 −0.0489633
\(622\) −463.103 + 463.103i −0.00119701 + 0.00119701i
\(623\) 106832. + 106832.i 0.275248 + 0.275248i
\(624\) 559977.i 1.43814i
\(625\) 227564. + 317494.i 0.582563 + 0.812786i
\(626\) −368.107 −0.000939345
\(627\) 382882. 382882.i 0.973934 0.973934i
\(628\) −187971. 187971.i −0.476620 0.476620i
\(629\) 401023.i 1.01360i
\(630\) −582.874 140.929i −0.00146857 0.000355073i
\(631\) −453999. −1.14024 −0.570120 0.821561i \(-0.693103\pi\)
−0.570120 + 0.821561i \(0.693103\pi\)
\(632\) 5415.87 5415.87i 0.0135592 0.0135592i
\(633\) −341208. 341208.i −0.851553 0.851553i
\(634\) 1605.90i 0.00399521i
\(635\) −159946. + 97661.2i −0.396667 + 0.242200i
\(636\) −888935. −2.19764
\(637\) 44641.8 44641.8i 0.110018 0.110018i
\(638\) −1191.14 1191.14i −0.00292632 0.00292632i
\(639\) 75294.2i 0.184400i
\(640\) −4587.61 7513.42i −0.0112002 0.0183433i
\(641\) 419719. 1.02151 0.510755 0.859727i \(-0.329366\pi\)
0.510755 + 0.859727i \(0.329366\pi\)
\(642\) −2939.31 + 2939.31i −0.00713141 + 0.00713141i
\(643\) −291772. 291772.i −0.705703 0.705703i 0.259926 0.965629i \(-0.416302\pi\)
−0.965629 + 0.259926i \(0.916302\pi\)
\(644\) 22695.3i 0.0547223i
\(645\) −10259.6 + 42433.4i −0.0246611 + 0.101997i
\(646\) 1701.00 0.00407604
\(647\) 123334. 123334.i 0.294628 0.294628i −0.544278 0.838905i \(-0.683196\pi\)
0.838905 + 0.544278i \(0.183196\pi\)
\(648\) −3798.79 3798.79i −0.00904681 0.00904681i
\(649\) 832203.i 1.97579i
\(650\) −2199.50 1129.64i −0.00520591 0.00267370i
\(651\) 319033. 0.752791
\(652\) −85546.1 + 85546.1i −0.201236 + 0.201236i
\(653\) 140737. + 140737.i 0.330052 + 0.330052i 0.852606 0.522554i \(-0.175021\pi\)
−0.522554 + 0.852606i \(0.675021\pi\)
\(654\) 3322.83i 0.00776878i
\(655\) 78167.1 + 18899.4i 0.182197 + 0.0440520i
\(656\) 444075. 1.03193
\(657\) 207114. 207114.i 0.479820 0.479820i
\(658\) −566.166 566.166i −0.00130765 0.00130765i
\(659\) 38660.5i 0.0890218i 0.999009 + 0.0445109i \(0.0141729\pi\)
−0.999009 + 0.0445109i \(0.985827\pi\)
\(660\) 724411. 442317.i 1.66302 1.01542i
\(661\) −252816. −0.578631 −0.289315 0.957234i \(-0.593428\pi\)
−0.289315 + 0.957234i \(0.593428\pi\)
\(662\) 1026.14 1026.14i 0.00234148 0.00234148i
\(663\) 479740. + 479740.i 1.09139 + 1.09139i
\(664\) 3533.56i 0.00801449i
\(665\) −61569.3 100836.i −0.139226 0.228020i
\(666\) −1674.71 −0.00377566
\(667\) 23773.4 23773.4i 0.0534366 0.0534366i
\(668\) −111971. 111971.i −0.250931 0.250931i
\(669\) 368356.i 0.823031i
\(670\) −666.035 + 2754.69i −0.00148370 + 0.00613653i
\(671\) −709579. −1.57600
\(672\) −2569.20 + 2569.20i −0.00568930 + 0.00568930i
\(673\) 322576. + 322576.i 0.712199 + 0.712199i 0.966995 0.254796i \(-0.0820083\pi\)
−0.254796 + 0.966995i \(0.582008\pi\)
\(674\) 4119.10i 0.00906740i
\(675\) 146693. 47141.9i 0.321961 0.103466i
\(676\) −85079.0 −0.186178
\(677\) 105500. 105500.i 0.230184 0.230184i −0.582586 0.812769i \(-0.697959\pi\)
0.812769 + 0.582586i \(0.197959\pi\)
\(678\) 1664.12 + 1664.12i 0.00362015 + 0.00362015i
\(679\) 114750.i 0.248893i
\(680\) 5183.41 + 1253.26i 0.0112098 + 0.00271033i
\(681\) −518534. −1.11811
\(682\) 3932.99 3932.99i 0.00845580 0.00845580i
\(683\) −424431. 424431.i −0.909841 0.909841i 0.0864179 0.996259i \(-0.472458\pi\)
−0.996259 + 0.0864179i \(0.972458\pi\)
\(684\) 246009.i 0.525823i
\(685\) 281262. 171735.i 0.599417 0.365997i
\(686\) −136.539 −0.000290141
\(687\) −534697. + 534697.i −1.13291 + 1.13291i
\(688\) 26594.2 + 26594.2i 0.0561836 + 0.0561836i
\(689\) 860439.i 1.81251i
\(690\) −254.909 417.480i −0.000535410 0.000876875i
\(691\) 240516. 0.503718 0.251859 0.967764i \(-0.418958\pi\)
0.251859 + 0.967764i \(0.418958\pi\)
\(692\) 525364. 525364.i 1.09710 1.09710i
\(693\) −140890. 140890.i −0.293368 0.293368i
\(694\) 2511.49i 0.00521449i
\(695\) 60857.1 251702.i 0.125992 0.521096i
\(696\) 3588.30 0.00740748
\(697\) −380445. + 380445.i −0.783117 + 0.783117i
\(698\) 633.403 + 633.403i 0.00130008 + 0.00130008i
\(699\) 500573.i 1.02450i
\(700\) −56661.6 176316.i −0.115636 0.359829i
\(701\) 451921. 0.919658 0.459829 0.888008i \(-0.347911\pi\)
0.459829 + 0.888008i \(0.347911\pi\)
\(702\) −689.661 + 689.661i −0.00139946 + 0.00139946i
\(703\) −233312. 233312.i −0.472091 0.472091i
\(704\) 731179.i 1.47529i
\(705\) −580904. 140452.i −1.16876 0.282586i
\(706\) −2325.58 −0.00466576
\(707\) −5370.55 + 5370.55i −0.0107443 + 0.0107443i
\(708\) 626741. + 626741.i 1.25032 + 1.25032i
\(709\) 567115.i 1.12818i −0.825713 0.564091i \(-0.809227\pi\)
0.825713 0.564091i \(-0.190773\pi\)
\(710\) −573.062 + 349.905i −0.00113680 + 0.000694118i
\(711\) −671016. −1.32738
\(712\) −3967.46 + 3967.46i −0.00782623 + 0.00782623i
\(713\) 78496.5 + 78496.5i 0.154409 + 0.154409i
\(714\) 1467.31i 0.00287822i
\(715\) −428138. 701189.i −0.837474 1.37159i
\(716\) 66521.1 0.129758
\(717\) 594646. 594646.i 1.15670 1.15670i
\(718\) 598.605 + 598.605i 0.00116116 + 0.00116116i
\(719\) 316359.i 0.611959i 0.952038 + 0.305979i \(0.0989838\pi\)
−0.952038 + 0.305979i \(0.901016\pi\)
\(720\) −90623.1 + 374813.i −0.174813 + 0.723018i
\(721\) 80501.6 0.154858
\(722\) −991.057 + 991.057i −0.00190118 + 0.00190118i
\(723\) 108513. + 108513.i 0.207589 + 0.207589i
\(724\) 777637.i 1.48354i
\(725\) −125339. + 244045.i −0.238456 + 0.464295i
\(726\) −4403.09 −0.00835381
\(727\) 9776.49 9776.49i 0.0184975 0.0184975i −0.697798 0.716295i \(-0.745836\pi\)
0.716295 + 0.697798i \(0.245836\pi\)
\(728\) 1657.88 + 1657.88i 0.00312818 + 0.00312818i
\(729\) 233328.i 0.439047i
\(730\) −2538.83 613.845i −0.00476418 0.00115189i
\(731\) −45567.2 −0.0852742
\(732\) 534392. 534392.i 0.997327 0.997327i
\(733\) 160398. + 160398.i 0.298533 + 0.298533i 0.840439 0.541906i \(-0.182297\pi\)
−0.541906 + 0.840439i \(0.682297\pi\)
\(734\) 1813.67i 0.00336641i
\(735\) −86982.7 + 53110.6i −0.161012 + 0.0983120i
\(736\) −1264.28 −0.00233392
\(737\) −665852. + 665852.i −1.22586 + 1.22586i
\(738\) 1588.78 + 1588.78i 0.00291710 + 0.00291710i
\(739\) 754750.i 1.38202i 0.722845 + 0.691010i \(0.242834\pi\)
−0.722845 + 0.691010i \(0.757166\pi\)
\(740\) −269529. 441425.i −0.492201 0.806109i
\(741\) 558217. 1.01664
\(742\) 1315.85 1315.85i 0.00239000 0.00239000i
\(743\) 212897. + 212897.i 0.385649 + 0.385649i 0.873132 0.487483i \(-0.162085\pi\)
−0.487483 + 0.873132i \(0.662085\pi\)
\(744\) 11848.1i 0.0214044i
\(745\) 21850.4 90372.0i 0.0393682 0.162825i
\(746\) 4618.82 0.00829953
\(747\) −218901. + 218901.i −0.392289 + 0.392289i
\(748\) 626447. + 626447.i 1.11965 + 1.11965i
\(749\) 301361.i 0.537184i
\(750\) 3022.64 + 2606.93i 0.00537358 + 0.00463454i
\(751\) −177487. −0.314693 −0.157347 0.987543i \(-0.550294\pi\)
−0.157347 + 0.987543i \(0.550294\pi\)
\(752\) −364069. + 364069.i −0.643795 + 0.643795i
\(753\) −382472. 382472.i −0.674543 0.674543i
\(754\) 1736.61i 0.00305464i
\(755\) 535189. + 129399.i 0.938887 + 0.227006i
\(756\) −73051.1 −0.127815
\(757\) −402096. + 402096.i −0.701678 + 0.701678i −0.964771 0.263093i \(-0.915258\pi\)
0.263093 + 0.964771i \(0.415258\pi\)
\(758\) −3042.86 3042.86i −0.00529594 0.00529594i
\(759\) 162527.i 0.282125i
\(760\) 3744.80 2286.53i 0.00648337 0.00395867i
\(761\) 374461. 0.646603 0.323301 0.946296i \(-0.395207\pi\)
0.323301 + 0.946296i \(0.395207\pi\)
\(762\) −1354.09 + 1354.09i −0.00233204 + 0.00233204i
\(763\) 170341. + 170341.i 0.292597 + 0.292597i
\(764\) 945238.i 1.61940i
\(765\) −243469. 398745.i −0.416027 0.681354i
\(766\) −3287.78 −0.00560331
\(767\) 606650. 606650.i 1.03121 1.03121i
\(768\) 550611. + 550611.i 0.933517 + 0.933517i
\(769\) 660539.i 1.11698i 0.829511 + 0.558490i \(0.188619\pi\)
−0.829511 + 0.558490i \(0.811381\pi\)
\(770\) −417.570 + 1727.05i −0.000704284 + 0.00291288i
\(771\) −479217. −0.806163
\(772\) −664361. + 664361.i −1.11473 + 1.11473i
\(773\) 166751. + 166751.i 0.279067 + 0.279067i 0.832737 0.553669i \(-0.186773\pi\)
−0.553669 + 0.832737i \(0.686773\pi\)
\(774\) 190.293i 0.000317645i
\(775\) −805804. 413851.i